When I started out with cloth diapers, I felt like I was fuddling through a world of all these special words and phrases. I figured out most okay, but each day I learn something new. As the adage goes, I wish I knew then what I knew now. I couldn't figure out why someone would choose one type over others. Hopefully this will make it a bit easier to figure out what you want and need.
Types of Diapers
Pockets--These are diapers that look similar to disposables. They have a pocket inside that you stuff with inserts to create different levels of absorbency (less for newborns or during the day, more for toddlers or overnight). They don't need a cover. These seem to be one of the most popular styles.
AIO (all in ones)--They are one piece, no stuffing, no liners, just put on and go. These are great for starting out, caregivers, dads, etc. With an older baby they're not super for overnights because you can't increase absorbency levels. They don't need a cover.
AI2 (all in two) or Hybrids--These are diapers that have a waterproof outer shell and interchangeable liners. These are good for reducing laundry and drying time. My experience so far is that they're not as absorbent (though adding an extra liner does help). They are called hybrids because they have an option for a disposable liner that is more eco friendly than regular disposable diapers.
Fitteds--These diapers are a more shapely alternative to prefolds. They need a diaper cover, though, either wool or plastic.
Prefolds--These are your standard, previous generations diapers. They need a diaper cover. Cheapest way to use cloth. Great for dust rags when they're retired (as anyone from previous generations will tell you).
Organic Cotton--average absorbency, average speed on absorbing (takes a LONG time to prep but works well)
Microfiber--fast but less absorbency, CANNOT be put directly against baby's skin
Hemp--absorbs a LOT but not terribly quickly
Fleece--often used as a soft barrier between baby and absorbent layers
Wool--used as a cover, doesn't have to be washed very often, waterproof but breathable
One Size--a diaper designed to fit from birth/small infancy to potty training. They might not work well for a newborn or a bigger potty trainer. Downside--more bulky
Sized--a diaper that has a specific size (S,M,L) based on weight. Slimmer/better fitting, but less versatility.
Snappi--basically this is the modern diaper pin (reminds me of an Ace Bandage clip)
Aplix/Velcro--brand names for hook and loop closures, good for getting a better fit and easy changes but can wear out more quickly and can be problematic when toddlers figure it out (as opposed to snaps)
I'm sure there is much more information out there, so much I've missed. With all the options out there, it can be very overwhelming. If you decide which options are most important to you right now, you can get started with any type. Once you've been doing it a bit, you'll find what you like and what you want. Our stash started with all AIOs for convenience. Then we added a handful of hybrids for extended outings. From here out, we'll get pockets to polish off our collection for variable absorbency as our little boy grows.